Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
15.1.723352547563839.1 | $x^{15} - x^{14} - 2 x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} + 5 x^{9} - 5 x^{8} + 4 x^{7} - 5 x^{6} - 4 x^{5} + 5 x^{4} - 2 x^{3} + x^{2} + x + 1$ | $-\,3^{3}\cdot 6653\cdot 4026880369$ | $S_{15}$ (as 15T104) | trivial |
15.1.3703260525677583.1 | $x^{15} - 2 x^{14} + x^{13} - x^{12} - 5 x^{11} + 4 x^{10} - 3 x^{9} + 2 x^{8} + 6 x^{7} - 3 x^{6} + 3 x^{5} - 4 x^{4} - 5 x^{3} - 3 x^{2} - 3 x - 1$ | $-\,3\cdot 13^{3}\cdot 561866260913$ | $S_{15}$ (as 15T104) | trivial |
15.1.5976545641547631.1 | $x^{15} - 2 x^{14} + 5 x^{13} - 10 x^{12} + 13 x^{11} - 20 x^{10} + 23 x^{9} - 22 x^{8} + 22 x^{7} - 20 x^{6} + 18 x^{5} - 20 x^{4} + 21 x^{3} - 15 x^{2} + 6 x - 1$ | $-\,3\cdot 195479\cdot 10191283363$ | $S_{15}$ (as 15T104) | trivial |
15.1.6401597515801839.1 | $x^{15} - x^{14} - x^{13} + 2 x^{12} - 4 x^{11} - x^{10} + 3 x^{9} + 3 x^{8} + 12 x^{7} - 2 x^{6} - 14 x^{5} + 7 x^{4} + 11 x^{3} - 6 x^{2} + 1$ | $-\,3^{9}\cdot 13^{3}\cdot 23^{6}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.1.24118280788986467.1 | $x^{15} - 2 x^{14} + 6 x^{12} - 13 x^{11} + 13 x^{10} - x^{9} - 21 x^{8} + 40 x^{7} - 41 x^{6} + 29 x^{5} - 18 x^{4} + 13 x^{3} - 7 x^{2} + x + 1$ | $-\,59^{6}\cdot 83^{3}$ | $S_5 \times S_3$ (as 15T29) | trivial |
15.1.44543599279432079.1 | $x^{15} - 4 x^{14} + 4 x^{13} + 4 x^{12} - 5 x^{11} - 13 x^{10} + 20 x^{9} + 4 x^{8} - 15 x^{7} - 13 x^{6} + 27 x^{5} - 4 x^{4} - 8 x^{3} - 2 x^{2} + 6 x - 1$ | $-\,239^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.57477829056511319.1 | $x^{15} - 2 x^{14} + 3 x^{13} - 3 x^{12} - 3 x^{11} + 6 x^{10} - 14 x^{9} + 4 x^{8} - 9 x^{7} - 7 x^{6} + 7 x^{5} - 15 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ | $-\,1609^{3}\cdot 13798511$ | $S_3^5.S_5$ (as 15T93) | trivial |
15.1.59770508839234803.1 | $x^{15} - 2 x^{12} + 3 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 1609^{3}$ | $C_3^4:(C_2\times S_5)$ (as 15T70) | trivial |
15.1.59770508839234803.2 | $x^{15} - x^{9} - x^{6} + x^{3} + 1$ | $-\,3^{15}\cdot 1609^{3}$ | $C_3^4:(C_2\times S_5)$ (as 15T70) | trivial |
15.1.69378727128301847.1 | $x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{12} + 2 x^{11} - 4 x^{10} + 3 x^{9} + 2 x^{8} + x^{7} - 5 x^{6} + 3 x^{5} + 3 x^{4} + 6 x^{3} + 2 x^{2} - 1$ | $-\,23^{5}\cdot 47^{6}$ | $D_5\times S_3$ (as 15T7) | trivial |
15.1.96318312824155136.1 | $x^{15} - 6 x^{14} + 19 x^{13} - 39 x^{12} + 58 x^{11} - 67 x^{10} + 68 x^{9} - 69 x^{8} + 65 x^{7} - 52 x^{6} + 33 x^{5} - 20 x^{4} + 12 x^{3} - 4 x^{2} + 3 x - 1$ | $-\,2^{10}\cdot 11^{7}\cdot 13^{6}$ | $D_5\times S_3$ (as 15T7) | trivial |
15.1.154669958288795403.1 | $x^{15} - x^{12} + 2 x^{9} - 3 x^{6} + 3 x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.2 | $x^{15} - 2 x^{12} + 2 x^{9} - x^{6} + 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.3 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.4 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.5 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.154669958288795403.6 | $x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ | $-\,3^{15}\cdot 47^{6}$ | $C_3^4:D_{10}$ (as 15T43) | trivial |
15.1.196421600341796875.1 | $x^{15} - x^{10} + 1$ | $-\,5^{15}\cdot 23^{5}$ | $C_5^2:(C_4\times S_3)$ (as 15T27) | trivial |
15.1.426781883555301359.1 | $x^{15} - x - 1$ | $-\,52489\cdot 418511\cdot 19428121$ | $S_{15}$ (as 15T104) | trivial |
15.1.449005897206417391.1 | $x^{15} + x - 1$ | $-\,7334881\cdot 61215157711$ | $S_{15}$ (as 15T104) | trivial |
15.1.677952124826430464.1 | $x^{15} - x^{14} + 4 x^{13} + 4 x^{11} - 2 x^{10} - 6 x^{9} - 12 x^{8} - 25 x^{7} + 19 x^{6} - 6 x^{5} + 28 x^{4} + 32 x^{3} - 36 x^{2} + 4 x + 4$ | $-\,2^{10}\cdot 131^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.873692352294921875.1 | $x^{15} + x^{5} - 1$ | $-\,5^{15}\cdot 31^{5}$ | $C_5^2:(C_4\times S_3)$ (as 15T27) | trivial |
15.1.957206371560558183.1 | $x^{15} - x^{14} + x^{13} - 6 x^{12} - 4 x^{11} + 5 x^{10} + 18 x^{9} + 23 x^{8} - 4 x^{5} + 4 x^{4} + 10 x^{3} - 5 x^{2} + 1$ | $-\,3^{12}\cdot 23^{9}$ | $A_5 \times S_3$ (as 15T23) | trivial |
15.1.957834337125359375.1 | $x^{15} - 6 x^{14} + 23 x^{13} - 67 x^{12} + 156 x^{11} - 307 x^{10} + 523 x^{9} - 771 x^{8} + 994 x^{7} - 1103 x^{6} + 1049 x^{5} - 854 x^{4} + 579 x^{3} - 288 x^{2} + 89 x - 13$ | $-\,5^{6}\cdot 11^{2}\cdot 47^{7}$ | $C_3^4:D_{15}$ (as 15T45) | trivial |
15.1.957834337125359375.2 | $x^{15} - 5 x^{14} + 15 x^{13} - 37 x^{12} + 74 x^{11} - 137 x^{10} + 207 x^{9} - 292 x^{8} + 353 x^{7} - 407 x^{6} + 396 x^{5} - 334 x^{4} + 222 x^{3} - 121 x^{2} + 44 x - 11$ | $-\,5^{6}\cdot 11^{2}\cdot 47^{7}$ | $C_3^4:D_{15}$ (as 15T45) | trivial |
15.1.100...407.1 | $x^{15} - 2 x^{14} - 3 x^{13} + 8 x^{12} + 4 x^{11} - 19 x^{10} + 3 x^{9} + 33 x^{8} - 23 x^{7} - 47 x^{6} + 39 x^{5} + 43 x^{4} - 13 x^{3} - 23 x^{2} - 8 x - 1$ | $-\,3^{6}\cdot 11^{8}\cdot 23^{5}$ | $((C_5^2 : C_3):C_2):C_2$ (as 15T18) | trivial |
15.1.108...475.1 | $x^{15} - x^{14} + 6 x^{13} - 8 x^{12} + 25 x^{11} - 40 x^{10} + 61 x^{9} - 74 x^{8} + 78 x^{7} - 83 x^{6} + 82 x^{5} - 36 x^{4} - 14 x^{3} + 35 x^{2} - 20 x + 5$ | $-\,5^{2}\cdot 17^{4}\cdot 43\cdot 2297^{3}$ | $S_3^5.S_5$ (as 15T93) | trivial |
15.1.115...192.1 | $x^{15} - 7 x^{14} + 29 x^{13} - 83 x^{12} + 185 x^{11} - 323 x^{10} + 445 x^{9} - 463 x^{8} + 341 x^{7} - 143 x^{6} + 3 x^{5} + 35 x^{4} - 15 x^{3} + x^{2} + 3 x - 1$ | $-\,2^{23}\cdot 13^{10}$ | $F_5 \times S_3$ (as 15T11) | trivial |
15.1.127...000.1 | $x^{15} - x^{14} + 3 x^{13} - x^{12} + 3 x^{11} + 5 x^{10} + 11 x^{9} + 11 x^{8} + 17 x^{7} + 19 x^{6} + 11 x^{5} + 11 x^{4} + 9 x^{3} + 3 x^{2} + x + 1$ | $-\,2^{22}\cdot 5^{6}\cdot 11^{7}$ | $A_5 \times S_3$ (as 15T23) | trivial |
15.1.219...096.1 | $x^{15} - 2 x^{14} + 5 x^{12} - 8 x^{11} + 2 x^{10} + 9 x^{9} - 11 x^{8} + 11 x^{6} - 7 x^{5} - 3 x^{4} + 7 x^{3} - x^{2} - 2 x + 1$ | $-\,2^{6}\cdot 34304987175946939$ | $S_{15}$ (as 15T104) | trivial |
15.1.267...712.1 | $x^{15} - 6 x^{13} - 6 x^{12} + 8 x^{9} + 24 x^{8} + 22 x^{7} - 16 x^{5} - 28 x^{4} - 42 x^{3} - 40 x^{2} - 20 x - 4$ | $-\,2^{37}\cdot 11^{7}$ | $F_5 \times S_3$ (as 15T11) | trivial |
15.1.314...479.1 | $x^{15} - 5 x^{14} + 11 x^{13} - 9 x^{12} - 7 x^{11} + 17 x^{10} - x^{9} - 29 x^{8} + 38 x^{7} - 13 x^{6} - 20 x^{5} + 24 x^{4} + 7 x^{3} - 23 x^{2} + 13 x - 1$ | $-\,439^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.386...075.1 | $x^{15} - 4 x^{12} + 5 x^{9} - 4 x^{6} + 6 x^{3} - 5$ | $-\,3^{15}\cdot 5^{2}\cdot 47^{6}$ | $C_3^5:D_{10}$ (as 15T55) | trivial |
15.1.386...075.2 | $x^{15} - 5 x^{12} + 10 x^{9} - 13 x^{6} + 13 x^{3} - 5$ | $-\,3^{15}\cdot 5^{2}\cdot 47^{6}$ | $C_3^5:D_{10}$ (as 15T55) | trivial |
15.1.494...375.1 | $x^{15} - 6 x^{12} + 9 x^{11} + 20 x^{10} + 57 x^{9} + 29 x^{8} + 27 x^{7} - 53 x^{6} - 44 x^{5} - 84 x^{4} - 43 x^{3} - 100 x^{2} - 75 x - 55$ | $-\,5^{10}\cdot 47^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.503...000.1 | $x^{15} - x^{10} + x^{5} + 1$ | $-\,2^{10}\cdot 5^{15}\cdot 11^{5}$ | $C_5^2:(C_4\times S_3)$ (as 15T27) | trivial |
15.1.602...616.1 | $x^{15} - 3 x^{14} + 10 x^{13} - 18 x^{12} + 41 x^{11} - 61 x^{10} + 57 x^{9} - 103 x^{8} + 29 x^{7} - 57 x^{6} + 17 x^{5} - 31 x^{4} + 12 x^{3} - 2 x^{2} + 3 x - 1$ | $-\,2^{10}\cdot 179^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.640...000.1 | $x^{15} - 5 x^{14} + 15 x^{13} - 35 x^{12} + 65 x^{11} - 93 x^{10} + 125 x^{9} - 125 x^{8} + 115 x^{7} - 55 x^{6} + 43 x^{5} + 5 x^{4} + 15 x^{3} + 5 x^{2} + 5 x - 1$ | $-\,2^{23}\cdot 5^{17}$ | $F_5 \times S_3$ (as 15T11) | trivial |
15.1.723...163.1 | $x^{15} - x^{12} + 3 x^{9} + 5 x^{6} - 6 x^{3} + 11$ | $-\,3^{15}\cdot 11^{2}\cdot 1609^{3}$ | $C_3^4:(S_3\times S_5)$ (as 15T83) | trivial |
15.1.172...067.1 | $x^{15} - 5 x^{12} + 4 x^{9} + 11 x^{6} - 5 x^{3} - 17$ | $-\,3^{15}\cdot 17^{2}\cdot 1609^{3}$ | $C_3^4:(S_3\times S_5)$ (as 15T83) | trivial |
15.1.318...272.1 | $x^{15} - 3 x^{14} - 4 x^{13} + 6 x^{12} + 20 x^{11} - 8 x^{10} + 10 x^{9} + 50 x^{8} - 45 x^{7} - 65 x^{6} + 106 x^{5} + 80 x^{4} - 20 x^{3} - 40 x^{2} - 20 x - 4$ | $-\,2^{10}\cdot 227^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.612...591.1 | $x^{15} - 3 x^{14} + 6 x^{13} - x^{12} - 20 x^{11} + 56 x^{10} - 81 x^{9} + 46 x^{8} + 90 x^{7} - 299 x^{6} + 481 x^{5} - 522 x^{4} + 403 x^{3} - 201 x^{2} + 44 x + 11$ | $-\,11^{7}\cdot 61^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.707...875.1 | $x^{15} - 3 x^{10} + 4 x^{5} - 3$ | $-\,3^{4}\cdot 5^{15}\cdot 31^{5}$ | $C_9^2\times C_{54}$ (as 15T49) | trivial |
15.1.707...875.2 | $x^{15} - 4 x^{10} + 5 x^{5} - 3$ | $-\,3^{4}\cdot 5^{15}\cdot 31^{5}$ | $C_9^2\times C_{54}$ (as 15T49) | trivial |
15.1.821...375.1 | $x^{15} - 5 x^{12} + 10 x^{11} - 12 x^{10} + 10 x^{9} - 20 x^{8} + 40 x^{7} - 60 x^{6} + 73 x^{5} - 65 x^{4} + 35 x^{3} - 35 x^{2} + 30 x - 9$ | $-\,5^{16}\cdot 7^{5}\cdot 179^{2}$ | $D_5\wr S_3$ (as 15T60) | trivial |
15.1.136...072.1 | $x^{15} - 5 x^{14} + 10 x^{13} - 10 x^{12} + 5 x^{11} - x^{10} - 4 x^{9} + 12 x^{8} - 12 x^{7} - 12 x^{6} + 32 x^{5} - 16 x^{4} - 32 x^{3} + 32 x^{2} - 32$ | $-\,2^{10}\cdot 47^{6}\cdot 179\cdot 257\cdot 269$ | $S_3\wr D_5$ (as 15T86) | trivial |
15.1.147...048.1 | $x^{15} - 2 x^{13} - 4 x^{12} + 2 x^{11} + 8 x^{10} + 7 x^{9} - 6 x^{8} - 12 x^{7} - 8 x^{6} + x^{5} + 10 x^{4} + 40 x^{3} + 80 x^{2} + 80 x + 32$ | $-\,2^{10}\cdot 11\cdot 47^{6}\cdot 1211333$ | $S_3\wr D_5$ (as 15T86) | trivial |
15.1.151...431.1 | $x^{15} - 3 x^{14} + 12 x^{13} - 5 x^{12} + 21 x^{11} + 15 x^{10} + 43 x^{9} + 54 x^{8} + 60 x^{7} + 93 x^{6} + 96 x^{5} + 108 x^{4} + 105 x^{3} + 72 x^{2} + 36 x + 9$ | $-\,3^{17}\cdot 53^{7}$ | $D_{15}$ (as 15T2) | trivial |
15.1.226...375.1 | $x^{15} - 4 x^{14} + 17 x^{13} - 53 x^{12} + 140 x^{11} - 315 x^{10} + 649 x^{9} - 1181 x^{8} + 2031 x^{7} - 3517 x^{6} + 5807 x^{5} - 7666 x^{4} + 7125 x^{3} - 4041 x^{2} + 1081 x + 47$ | $-\,5^{6}\cdot 13^{4}\cdot 47^{7}$ | $C_3^4:D_5$ (as 15T35) | trivial |
15.1.238...375.1 | $x^{15} - 5 x^{14} + 9 x^{13} - 11 x^{12} + 24 x^{11} - 54 x^{10} + 89 x^{9} - 73 x^{8} - 58 x^{7} + 102 x^{6} + 74 x^{5} - 58 x^{4} - 35 x^{3} - 230 x^{2} + 325 x - 125$ | $-\,5^{7}\cdot 163^{7}$ | $D_{15}$ (as 15T2) | trivial |